Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ..draughtsmen .. . investigate thepaths described by points during their rolling,t From CardU, the Latin for heart. SPECIAL TROCHOIDS. 63 F T^R Q (traced by point F as carried bj the given generator) in a point T^. The angle T^ R Fwill then be one-third of NR F, which may be proved as follows: F reaches T^ by the rolling ofarc m n on arc m 1\. These arcs are subtended bj^ equal angles, 4>, the circles being equal. Duringthis rolling R reaches R^, bringing i? i^
Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ..draughtsmen .. . investigate thepaths described by points during their rolling,t From CardU, the Latin for heart. SPECIAL TROCHOIDS. 63 F T^R Q (traced by point F as carried bj the given generator) in a point T^. The angle T^ R Fwill then be one-third of NR F, which may be proved as follows: F reaches T^ by the rolling ofarc m n on arc m 1\. These arcs are subtended bj^ equal angles, 4>, the circles being equal. Duringthis rolling R reaches R^, bringing i? i^ to R^ T^. In the triangles Ti R^ F and R F R^ the sideF Ri is common, angles <^ equal and side R^ T^ equal to side R F; the line R T^ is thereforeparallel to Ri F, whence angle T^ R F must also equal <^. In the triangle R F R^ we denote by 6 180° —^ 1S0° or 6 = 2 In triangle NR F we have the angle at F equal to 6 — <^, and J {6 — <^) + .r + <^ = 180° which gives x ^= 2 by substituting value of 6 from previous equation. xlg-. loe. FOT_Cardioid. 186. The Involute. As the opposite extreme of a circle rolling on a straight line we may havethe latter rolHng on a circle. In this case the rolling circle has an infinite radius. A point on thestraight line describes a curve called the involute. This would be the path of the end of a threadif the latter were in tension while being unwound irom a spool. In Fig. 107 a rule is shown, tangent at u to a circle on which it is supposed to roll. Were apencil-point inserted in the centre of the circle at j (which is on line m x produced) it would tracethe involute. When j reaches a the rule will have had rolling contact with the base circle over anarc uts—a whose length equals Une u x j. Were a the initial point we may obtain b, c, etc., bjmaking tangent m h = arc in a; tangent n c ^ arc n a, etc. Each tangent thus equals the arc frominitial point to i^oint of tangency. 64 THEORETICAL AND PRACTICAL GRAPHICS. 187. The ci
Size: 1637px × 1527px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1890, booksubjec, booksubjectlettering
